DLMF:18.7.E25 (Q5593)

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DLMF:18.7.E25
No description defined

    Statements

    Defining formula
    lim λ → 0 ⁡ 1 λ ⁢ C n ( λ ) ⁡ ( x ) = 2 n ⁢ T n ⁡ ( x ) , subscript → 𝜆 0 1 𝜆 ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 2 𝑛 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle\lim_{\lambda\to 0}\frac{1}{\lambda}C^{(\lambda)}_% {n}\left(x\right)=\frac{2}{n}T_{n}\left(x\right),}}
    0 references
    DLMF id
    DLMF:18.7.E25
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    constraint
    n ≥ 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}
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    Symbols used
    Q11207
    Defining formula
    T n ⁡ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r4.m2acdec
    0 references
    Q11475
    Defining formula
    C n ( λ ) ⁡ ( x ) ultraspherical-Gegenbauer-polynomial 𝜆 𝑛 𝑥 {\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r3.m2agdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1xdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1xdec
    0 references
     
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